Calculate the Average: Finding Mean of 20, 0, and 7

Q: Should I include zero when calculating the average?

Yes, absolutely! Zero is a valid number and must be included in both the sum and the count. Even though it doesn't change the sum, it affects the final average.

Q: Why doesn't zero affect the sum but still matters?

Zero doesn't change the sum (20 + 0 + 7 = 27), but it increases the count of numbers from 2 to 3. This makes the average smaller because you're dividing by a larger number!

Q: What if I accidentally forgot to count the zero?

You'd get $ \frac{27}{2} = 13.5 $ instead of the correct answer 9. Always list out all numbers first to make sure you count them properly.

Q: Is there a quick way to check if my average is reasonable?

Yes! Your average should be between the smallest and largest values. Since we have 0, 7, and 20, the average (9) should fall between 0 and 20, which it does.

Q: Can the average be the same as one of the original numbers?

Yes! In this case, our average of 9 happens to be close to (but not exactly) one of our numbers (7). This is completely normal and depends on the specific values.

Mean Calculation with Zero Values

Calculate the average

of $20$ , $0$ , and $7$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the average

00:03 To calculate the average, we need to divide the sum by the number of occurrences

00:06 Let's sum up the numbers

00:13 and divide by the number of occurrences (3)

00:30 and this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the average

of $20$ , $0$ , and $7$ .

Step-by-step solution

The average of a set of numbers is found by dividing the sum of the numbers by how many numbers there are.

Let's find the average of the numbers $20$ , $0$ , and $7$ :

Step 1: Calculate the sum of the numbers:
$20 + 0 + 7 = 27$ .
Step 2: Count how many numbers there are. Here, we have 3 numbers.
Step 3: Apply the average formula:
$\text{Average} = \frac{27}{3}$ .
Step 4: Divide the sum by 3:
$\frac{27}{3} = 9$ .

Therefore, the average of 20, 0, and 7 is $9$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of all numbers divided by count
Technique: Add all values first: 20 + 0 + 7 = 27
Check: Verify by multiplying: 9 × 3 should equal 27 ✓

Common Mistakes

Avoid these frequent errors

Ignoring zero when counting numbers
Don't skip the zero and divide by 2 instead of 3 = $\frac{27}{2} = 13.5$ ! Zero is still a number that must be counted. Always include all numbers in your count, even zeros.

Practice Quiz

Test your knowledge with interactive questions

If the balls below are divided so that each column in the table contains an equal number, then how many balls will there be in each column?

FAQ

Everything you need to know about this question

Should I include zero when calculating the average?

Yes, absolutely! Zero is a valid number and must be included in both the sum and the count. Even though it doesn't change the sum, it affects the final average.

Why doesn't zero affect the sum but still matters?

Zero doesn't change the sum (20 + 0 + 7 = 27), but it increases the count of numbers from 2 to 3. This makes the average smaller because you're dividing by a larger number!

What if I accidentally forgot to count the zero?

You'd get $\frac{27}{2} = 13.5$ instead of the correct answer 9. Always list out all numbers first to make sure you count them properly.

Is there a quick way to check if my average is reasonable?

Yes! Your average should be between the smallest and largest values. Since we have 0, 7, and 20, the average (9) should fall between 0 and 20, which it does.

Can the average be the same as one of the original numbers?

Yes! In this case, our average of 9 happens to be close to (but not exactly) one of our numbers (7). This is completely normal and depends on the specific values.

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